Powerlaw flux

[3]:
# Parameters
func_name = "Powerlaw_flux"
wide_energy_range = True
x_scale = "log"
y_scale = "log"
linear_range = False

Description

[5]:
func.display()
  • description: A simple power-law with the photon flux in a band used as normalization. This will reduce the correlation between the index and the normalization.
  • formula: $ \frac{F(\gamma+1)} {b^{\gamma+1} - a^{\gamma+1}} (x)^{\gamma}$
  • parameters:
    • F:
      • value: 1.0
      • desc: Integral between a and b
      • min_value: 1e-30
      • max_value: 1000.0
      • unit:
      • is_normalization: True
      • delta: 0.1
      • free: True
    • index:
      • value: -2.0
      • desc: Photon index
      • min_value: -10.0
      • max_value: 10.0
      • unit:
      • is_normalization: False
      • delta: 0.2
      • free: True
    • a:
      • value: 1.0
      • desc: lower bound for the band in which computing the integral F
      • min_value: None
      • max_value: None
      • unit:
      • is_normalization: False
      • delta: 0.1
      • free: False
    • b:
      • value: 100.0
      • desc: upper bound for the band in which computing the integral F
      • min_value: None
      • max_value: None
      • unit:
      • is_normalization: False
      • delta: 10.0
      • free: False

Shape

The shape of the function.

If this is not a photon model but a prior or linear function then ignore the units as these docs are auto-generated

[6]:
fig, ax = plt.subplots()


ax.plot(energy_grid, func(energy_grid), color=blue)

ax.set_xlabel("energy (keV)")
ax.set_ylabel("photon flux")
ax.set_xscale(x_scale)
ax.set_yscale(y_scale)

../_images/notebooks_Powerlaw_flux_8_0.png

F\(_{\nu}\)

The F\(_{\nu}\) shape of the photon model if this is not a photon model, please ignore this auto-generated plot

[7]:
fig, ax = plt.subplots()

ax.plot(energy_grid, energy_grid * func(energy_grid), red)


ax.set_xlabel("energy (keV)")
ax.set_ylabel(r"energy flux (F$_{\nu}$)")
ax.set_xscale(x_scale)
ax.set_yscale(y_scale)


../_images/notebooks_Powerlaw_flux_10_0.png

\(\nu\)F\(_{\nu}\)

The \(\nu\)F\(_{\nu}\) shape of the photon model if this is not a photon model, please ignore this auto-generated plot

[8]:
fig, ax = plt.subplots()

ax.plot(energy_grid, energy_grid**2 * func(energy_grid), color=green)


ax.set_xlabel("energy (keV)")
ax.set_ylabel(r"$\nu$F$_{\nu}$")
ax.set_xscale(x_scale)
ax.set_yscale(y_scale)

../_images/notebooks_Powerlaw_flux_12_0.png